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This paper presents a differential game approach to formation control of mobile robots. The formation control is formulated as a linear-quadratic Nash differential game through the use of graph theory. Finite horizon cost function is discussed under the open-loop information structure. An open-loop Nash equilibrium solution is investigated by establishing existence and stability conditions of the solutions of coupled (asymmetrical) Riccati differential equations. Based on the finite horizon open-loop Nash equilibrium solution, a receding horizon approach is adopted to synthesize a state-feedback controller for the formation control. Mobile robots with double integrator dynamics are used in the formation control simulation. Simulation results are provided to justify the models and solutions.